





import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
def 							a_	(    __magic_name__		,     __magic_name__=0.999		,     __magic_name__="cosine"		,     )				->			List[str]:




				"""simple docstring"""






				if alpha_transform_type == "cosine":

								def alpha_bar_fn(__magic_name__   ):
												return math.cos((t + 0.008) / 1.008 * math.pi / 2   ) ** 2

				elif alpha_transform_type == "exp":

								def alpha_bar_fn(__magic_name__   ):
												return math.exp(t * -12.0   )

				else:
								raise ValueError(F"Unsupported alpha_tranform_type: {alpha_transform_type}"   )

				snake_case   :					Optional[int]    						=				[]
				for i in range(a_   ):
								snake_case   :					Dict    						=				i / num_diffusion_timesteps
								snake_case   :					List[Any]    						=				(i + 1) / num_diffusion_timesteps
								betas.append(min(1 - alpha_bar_fn(a_   ) / alpha_bar_fn(a_   )		,     a_   )   )
				return torch.tensor(a_		,     dtype=torch.floataa   )
class   a_ (			_A		,							_A      ):
			A__      :			str       	=  [e.name for e in KarrasDiffusionSchedulers]
			A__      :			Any       	=  2

			@register_to_config
			def __init__(   self   :  str     , UpperCAmelCase__   :  Optional[int] = 1_000     , UpperCAmelCase__   :  str = 0.0_0085     , UpperCAmelCase__   :  Optional[int] = 0.012     , UpperCAmelCase__   :  Tuple = "linear"     , UpperCAmelCase__   :  int = None     , UpperCAmelCase__   :  str = "epsilon"     , UpperCAmelCase__   :  str = False     , UpperCAmelCase__   :  List[Any] = False     , UpperCAmelCase__   :  Any = 1.0     , UpperCAmelCase__   :  Union[str, Any] = "linspace"     , UpperCAmelCase__   :  Tuple = 0     , ):






							"""simple docstring"""
							if trained_betas is not None:
											snake_case   :					List[Any]    						=				torch.tensor(a_     , dtype=torch.floataa						)
							elif beta_schedule == "linear":
											snake_case   :					List[str]    						=				torch.linspace(a_     , a_     , a_     , dtype=torch.floataa						)
							elif beta_schedule == "scaled_linear":
											# this schedule is very specific to the latent diffusion model.
											snake_case   :					List[str]    						=				(
											    torch.linspace(beta_start**0.5     , beta_end**0.5     , a_     , dtype=torch.floataa						) ** 2
											)
							elif beta_schedule == "squaredcos_cap_v2":
											# Glide cosine schedule
											snake_case   :					List[Any]    						=				betas_for_alpha_bar(a_     , alpha_transform_type='''cosine'''						)
							elif beta_schedule == "exp":
											snake_case   :					Any    						=				betas_for_alpha_bar(a_     , alpha_transform_type='''exp'''						)
							else:
											raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"						)

							snake_case   :					Optional[int]    						=				1.0 - self.betas
							snake_case   :					Optional[Any]    						=				torch.cumprod(self.alphas     , dim=0						)

							#  set all values
							self.set_timesteps(a_     , a_     , a_						)
							snake_case   :					Union[str, Any]    						=				use_karras_sigmas

			def      lowerCAmelCase(   self   :  Tuple     , UpperCAmelCase__   :  Optional[int]     , UpperCAmelCase__   :  Any=None						):






							"""simple docstring"""
							if schedule_timesteps is None:
											snake_case   :					List[str]    						=				self.timesteps

							snake_case   :					int    						=				(schedule_timesteps == timestep).nonzero()

							# The sigma index that is taken for the **very** first `step`
							# is always the second index (or the last index if there is only 1)
							# This way we can ensure we don't accidentally skip a sigma in
							# case we start in the middle of the denoising schedule (e.g. for image-to-image)
							if len(self._index_counter						) == 0:
											snake_case   :					Union[str, Any]    						=				1 if len(a_						) > 1 else 0
							else:
											snake_case   :					Tuple    						=				timestep.cpu().item() if torch.is_tensor(a_						) else timestep
											snake_case   :					Any    						=				self._index_counter[timestep_int]

							return indices[pos].item()

			@property
			def      lowerCAmelCase(   self   :  Union[str, Any]						):






							"""simple docstring"""
							# standard deviation of the initial noise distribution
							if self.config.timestep_spacing in ["linspace", "trailing"]:
											return self.sigmas.max()

							return (self.sigmas.max() ** 2 + 1) ** 0.5

			def      lowerCAmelCase(   self   :  Dict     , UpperCAmelCase__   :  Dict     , UpperCAmelCase__   :  Dict     , ):






							"""simple docstring"""
							snake_case   :					Union[str, Any]    						=				self.index_for_timestep(a_						)

							snake_case   :					Any    						=				self.sigmas[step_index]
							snake_case   :					int    						=				sample / ((sigma**2 + 1) ** 0.5)
							return sample

			def      lowerCAmelCase(   self   :  List[Any]     , UpperCAmelCase__   :  Union[str, Any]     , UpperCAmelCase__   :  int = None     , UpperCAmelCase__   :  Union[str, Any] = None     , ):






							"""simple docstring"""
							snake_case   :					List[Any]    						=				num_inference_steps

							snake_case   :					Optional[int]    						=				num_train_timesteps or self.config.num_train_timesteps

							# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
							if self.config.timestep_spacing == "linspace":
											snake_case   :					Optional[Any]    						=				np.linspace(0     , num_train_timesteps - 1     , a_     , dtype=a_						)[::-1].copy()
							elif self.config.timestep_spacing == "leading":
											snake_case   :					str    						=				num_train_timesteps // self.num_inference_steps
											# creates integer timesteps by multiplying by ratio
											# casting to int to avoid issues when num_inference_step is power of 3
											snake_case   :					Dict    						=				(np.arange(0     , a_						) * step_ratio).round()[::-1].copy().astype(a_						)
											timesteps += self.config.steps_offset
							elif self.config.timestep_spacing == "trailing":
											snake_case   :					Tuple    						=				num_train_timesteps / self.num_inference_steps
											# creates integer timesteps by multiplying by ratio
											# casting to int to avoid issues when num_inference_step is power of 3
											snake_case   :					int    						=				(np.arange(a_     , 0     , -step_ratio						)).round().copy().astype(a_						)
											timesteps -= 1
							else:
											raise ValueError(
											    F"{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'."						)

							snake_case   :					Any    						=				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
							snake_case   :					Any    						=				np.log(a_						)
							snake_case   :					int    						=				np.interp(a_     , np.arange(0     , len(a_						)						)     , a_						)

							if self.config.use_karras_sigmas:
											snake_case   :					int    						=				self._convert_to_karras(in_sigmas=a_     , num_inference_steps=self.num_inference_steps						)
											snake_case   :					Any    						=				np.array([self._sigma_to_t(a_     , a_						) for sigma in sigmas]						)

							snake_case   :					int    						=				np.concatenate([sigmas, [0.0]]						).astype(np.floataa						)
							snake_case   :					int    						=				torch.from_numpy(a_						).to(device=a_						)
							snake_case   :					Any    						=				torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2						), sigmas[-1:]]						)

							snake_case   :					Union[str, Any]    						=				torch.from_numpy(a_						)
							snake_case   :					Union[str, Any]    						=				torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2						)]						)

							if str(a_						).startswith('''mps'''						):
											# mps does not support float64
											snake_case   :					str    						=				timesteps.to(a_     , dtype=torch.floataa						)
							else:
											snake_case   :					int    						=				timesteps.to(device=a_						)

							# empty dt and derivative
							snake_case   :					Union[str, Any]    						=				None
							snake_case   :					Optional[Any]    						=				None

							# for exp beta schedules, such as the one for `pipeline_shap_e.py`
							# we need an index counter
							snake_case   :					int    						=				defaultdict(a_						)

			def      lowerCAmelCase(   self   :  int     , UpperCAmelCase__   :  Tuple     , UpperCAmelCase__   :  Tuple						):






							"""simple docstring"""
							# get log sigma
							snake_case   :					str    						=				np.log(a_						)

							# get distribution
							snake_case   :					int    						=				log_sigma - log_sigmas[:, np.newaxis]

							# get sigmas range
							snake_case   :					int    						=				np.cumsum((dists >= 0)     , axis=0						).argmax(axis=0						).clip(max=log_sigmas.shape[0] - 2						)
							snake_case   :					Any    						=				low_idx + 1

							snake_case   :					str    						=				log_sigmas[low_idx]
							snake_case   :					Optional[Any]    						=				log_sigmas[high_idx]

							# interpolate sigmas
							snake_case   :					Optional[Any]    						=				(low - log_sigma) / (low - high)
							snake_case   :					List[str]    						=				np.clip(a_     , 0     , 1						)

							# transform interpolation to time range
							snake_case   :					int    						=				(1 - w) * low_idx + w * high_idx
							snake_case   :					Dict    						=				t.reshape(sigma.shape						)
							return t

			def      lowerCAmelCase(   self   :  Optional[Any]     , UpperCAmelCase__   :  Dict     , UpperCAmelCase__   :  List[Any]						):






							"""simple docstring"""
							snake_case   :					float    						=				in_sigmas[-1].item()
							snake_case   :					float    						=				in_sigmas[0].item()

							snake_case   :					str    						=				7.0  # 7.0 is the value used in the paper
							snake_case   :					Optional[int]    						=				np.linspace(0     , 1     , a_						)
							snake_case   :					Optional[int]    						=				sigma_min ** (1 / rho)
							snake_case   :					str    						=				sigma_max ** (1 / rho)
							snake_case   :					List[str]    						=				(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
							return sigmas

			@property
			def      lowerCAmelCase(   self   :  Optional[int]						):






							"""simple docstring"""
							return self.dt is None

			def      lowerCAmelCase(   self   :  List[Any]     , UpperCAmelCase__   :  int     , UpperCAmelCase__   :  str     , UpperCAmelCase__   :  int     , UpperCAmelCase__   :  List[str] = True     , ):






							"""simple docstring"""
							snake_case   :					Optional[int]    						=				self.index_for_timestep(a_						)

							# advance index counter by 1
							snake_case   :					List[str]    						=				timestep.cpu().item() if torch.is_tensor(a_						) else timestep
							self._index_counter[timestep_int] += 1

							if self.state_in_first_order:
											snake_case   :					Optional[Any]    						=				self.sigmas[step_index]
											snake_case   :					Dict    						=				self.sigmas[step_index + 1]
							else:
											# 2nd order / Heun's method
											snake_case   :					List[str]    						=				self.sigmas[step_index - 1]
											snake_case   :					int    						=				self.sigmas[step_index]

							# currently only gamma=0 is supported. This usually works best anyways.
							# We can support gamma in the future but then need to scale the timestep before
							# passing it to the model which requires a change in API
							snake_case   :					int    						=				0
							snake_case   :					Optional[int]    						=				sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

							# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
							if self.config.prediction_type == "epsilon":
											snake_case   :					int    						=				sigma_hat if self.state_in_first_order else sigma_next
											snake_case   :					Tuple    						=				sample - sigma_input * model_output
							elif self.config.prediction_type == "v_prediction":
											snake_case   :					List[str]    						=				sigma_hat if self.state_in_first_order else sigma_next
											snake_case   :					int    						=				model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
											    sample / (sigma_input**2 + 1)
											)
							elif self.config.prediction_type == "sample":
											snake_case   :					Optional[int]    						=				model_output
							else:
											raise ValueError(
											    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"						)

							if self.config.clip_sample:
											snake_case   :					Optional[int]    						=				pred_original_sample.clamp(
											    -self.config.clip_sample_range     , self.config.clip_sample_range						)

							if self.state_in_first_order:
											# 2. Convert to an ODE derivative for 1st order
											snake_case   :					Union[str, Any]    						=				(sample - pred_original_sample) / sigma_hat
											# 3. delta timestep
											snake_case   :					Optional[int]    						=				sigma_next - sigma_hat

											# store for 2nd order step
											snake_case   :					List[str]    						=				derivative
											snake_case   :					Optional[int]    						=				dt
											snake_case   :					Dict    						=				sample
							else:
											# 2. 2nd order / Heun's method
											snake_case   :					Dict    						=				(sample - pred_original_sample) / sigma_next
											snake_case   :					Optional[int]    						=				(self.prev_derivative + derivative) / 2

											# 3. take prev timestep & sample
											snake_case   :					Optional[int]    						=				self.dt
											snake_case   :					Tuple    						=				self.sample

											# free dt and derivative
											# Note, this puts the scheduler in "first order mode"
											snake_case   :					Tuple    						=				None
											snake_case   :					Optional[Any]    						=				None
											snake_case   :					Union[str, Any]    						=				None

							snake_case   :					Any    						=				sample + derivative * dt

							if not return_dict:
											return (prev_sample,)

							return SchedulerOutput(prev_sample=a_						)

			def      lowerCAmelCase(   self   :  Tuple     , UpperCAmelCase__   :  List[Any]     , UpperCAmelCase__   :  Union[str, Any]     , UpperCAmelCase__   :  List[Any]     , ):






							"""simple docstring"""
							# Make sure sigmas and timesteps have the same device and dtype as original_samples
							snake_case   :					Tuple    						=				self.sigmas.to(device=original_samples.device     , dtype=original_samples.dtype						)
							if original_samples.device.type == "mps" and torch.is_floating_point(a_						):
											# mps does not support float64
											snake_case   :					Optional[int]    						=				self.timesteps.to(original_samples.device     , dtype=torch.floataa						)
											snake_case   :					Dict    						=				timesteps.to(original_samples.device     , dtype=torch.floataa						)
							else:
											snake_case   :					List[Any]    						=				self.timesteps.to(original_samples.device						)
											snake_case   :					str    						=				timesteps.to(original_samples.device						)

							snake_case   :					Tuple    						=				[self.index_for_timestep(a_     , a_						) for t in timesteps]

							snake_case   :					Dict    						=				sigmas[step_indices].flatten()
							while len(sigma.shape						) < len(original_samples.shape						):
											snake_case   :					Any    						=				sigma.unsqueeze(-1						)

							snake_case   :					str    						=				original_samples + noise * sigma
							return noisy_samples



			def __len__(   self   :  Optional[int]						):






							"""simple docstring"""
							return self.config.num_train_timesteps







'''simple docstring'''






from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst






def   __A    (				):
		lowerCAmelCase						,		lowerCAmelCase  :     List[Any]       						= 9, 1_4  # noqa: F841
		lowerCAmelCase  :     int       						= [
		    [0, 1, 4],
		    [0, 7, 8],
		    [1, 2, 8],
		    [7, 8, 7],
		    [7, 6, 1],
		    [2, 8, 2],
		    [8, 6, 6],
		    [2, 3, 7],
		    [2, 5, 4],
		    [6, 5, 2],
		    [3, 5, 1_4],
		    [3, 4, 9],
		    [5, 4, 1_0],
		    [1, 7, 1_1],
		]

		lowerCAmelCase  :     Optional[Any]       						= defaultdict(a_						)
		for nodea, nodea, cost in edges:
				adjancency[nodea].append([nodea, cost]						)
				adjancency[nodea].append([nodea, cost]						)

		lowerCAmelCase  :     int       						= mst(a_						)

		lowerCAmelCase  :     Tuple       						= [
		    [7, 6, 1],
		    [2, 8, 2],
		    [6, 5, 2],
		    [0, 1, 4],
		    [2, 5, 4],
		    [2, 3, 7],
		    [0, 7, 8],
		    [3, 4, 9],
		]

		for answer in expected:
				lowerCAmelCase  :     List[str]       						= tuple(answer[:2]						)
				lowerCAmelCase  :     int       						= tuple(edge[::-1]						)
				assert edge in result or reverse in result



